3.1 Author and Date
The only option ever proposed in the Early Church was the apostle Matthew called by Jesus in Matthew 9:9; Matthew 10:3. Papias, bishop of Hierapolis (died c. A.D. 130) made this statement about Matthew, known as “the Papias Logion” which survives only in Eusebius (Hist. Eccl. 3.39.16). “Matthew collected (synetaxato) the oracles (ta logia) in the Hebrew language (Hebraidi dialektō), and each interpreted (hērmēneusen) them as best he could.” Earlier generations understood this to say that Matthew wrote in either Hebrew or Aramaic, and the Gospel as we have it was later translated into Greek. However the phrase is now generally thought to mean instead “in the Hebrew style”. Irenaeus added that the First Gospel was composed while Peter and Paul were founding the church in Rome (Haer. 3.1.1; from Eusebius, Hist. Eccl. 5.8.2). Eusebius and Origen (Hist. Eccl. 6.25.4) agreed
Some argue that Matthew (an apostle) would not have used Mark (not an apostle) but that objection does not stand if Peter (chief apostle) was Mark’s main source and authority. Known as Levi (a Jewish name) in Mark 2:14-15 and Luke 5:27-29 the Gospel-writer was most probably a Jew but as a tax-collector, he would have been fluent in Greek. Many scholars support apostolic authorship including Tasker, Albright and Mann, Maier, Gundry, Carson, and France.
Several passages in Matthew imply that the Temple in Jerusalem was still standing when they were written – Matthew 5:23–24; 17:24–27; 23:16–22). After the destruction of the Temple in 70 AD Emperor Vespasian replaced the temple tax with a “Jewish tax” for the treasury of the temple in Jerusalem. It is unlikely Matthew would have included as story encouraging Christians to pay such a tax to support pagan worship Matthew 17:24-27. So although many would date Matthew after 70 AD it is credible to suggest the late 60s AD (see commentary by R.T.France).

3.2 Themes in Matthew’s Gospel
3.2.1 Jesus is God’s Messiah who fulfills OT promises, reveals God’s will and inaugurates the kingdom of heaven through his public ministry, passion and resurrection, and consequently, reigns over the new people of God.
Jesus is given the title Messiah in Matthew 1:1, 16, 17, 18; 2:4; 11:2; 16:16, 20; 22:42; 23:10; 26:63, 68; 27:17, 22. In Jesus the OT promises of restoration and salvation are coming to pass (cf. 2:4; 26:63) fulfilling the OT in his person and ministry (see below). For Matthew the term Messiah seems to imply preexistence (2:4; 22:41–46). Jesus as Lord – evidenced by worship offered to Jesus as one who alone has divine power. Matthew 8:2, 6, 25; 9:28; perhaps also 2:2; 8:11; 14:33.
3.2.2 Jesus the Teacher
Jesus’s own description of himself Matthew 10:24, 25; 23:8; 26:18
Called “teacher” by others Matthew 8:19; 9:11; 12:38; 17:24; 19:16; 22:16, 24, 36
Jesus’s ethical teaching – especially the Sermon on the Mount chapters 5-7 and see also 13 and 18.
3.2.1 Discipleship
3.2.2 Matthew is the most “ecclesiastical” Gospel. Matthew 16:17-19; 18:15-20
Perhaps offering a “Manual of Discipline” for the church (Stendahl) e.g. on divorce 5:31-33, disputes 18:15-20, discipline 18:18; 16:9 in a “mixed membership” church 7:15-27; 13:24ff.

3.3 Special theme in Matthew’s Gospel – The Fulfilment of God’s Promises to the Jews in the Life and Ministry of Jesus
3.3.1 The Prologue – Genealogy, Davidic Kingship, Virgin Birth Matthew 1-2
3.3.2 Formula Quotations: “All this took place so that … “ Not always obvious quotes from MT or LXX, sometimes from Targums, including editorial comments.
Matthew 1:22-23 (Isaiah 7:14) 2:5-6 (Micah 5:2) 2:15 (Hosea 11:1) 2:17-18 (Jeremiah 31:15) 2:23 (“Nazarene” not a quote) 4:14-16 (Isaiah 9:1-2) 8:17 (Isaiah 53:4) 12:17-21 (Isaiah 42:1-4) 13:35 (Psalm 78:2) 21:4-5 (Zechariah 9:9) 27:9-10 Judas’s death echoes of Zechariah and Jeremiah.
3.3.3 Other Quotations from the Old Testament in Matthew
Matthew 3:3 (Isaiah 40:3) 11:11 Malachi 3:1 13:14 (Isaiah 6:9-10) 21:16 (Psalm 8) 21:42 (Psalm 118:22-23)
3.3.4 Jesus fulfilling the Law Matthew 5:17
3.3.5 Jesus reshaping the Law Matthew 5:17-46; 12:1-14; Chapters 21-22
3.3.6 Jesus cleanses and renews the Temple Matthew 21:13
3.3.7 Typology – a pattern (type) in the OT echoed in NT (antitype).
Jesus is a sort of new Moses e.g. 2:22. He brings a new Exodus, and he is a kind of new Israel (c.f. Hosea 11:1 in Matthew 1:18–2:23; 3:3). In Matthew 4 Jesus as Son of God is being tested as Israel was in Deuteronomy. Jesus is like David 12:3-4, Priests 12:5-6, Jonah 12:39-41, Solomon 12:42. Jesus is like Elisha 14:15f, Isaiah Mt 13:13. Matthew 21:42 quotes Psalm 118 Matthew 27:46 echoes Psalm 22. The disciples are portrayed as a new Israel in Matthew 21, also 5:48, 5:5, 8:11-12, 26:31, 19:28, 26:28. So Jesus is in line with OT, but also superior to the OT and the fulfilment of the OT, bringing in the promised Messianic Age.